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One use case is in theoretical physics, where expressions that take up about a terabyte are generated when computing Feynman diagrams, but only in the intermedi

One use case is in theoretical physics, where expressions that take up about a terabyte are generated when computing Feynman diagrams, but only in the intermediate stages. By the end of a two-month computation you get a result similar to equation 4.5 in this paper: https://arxiv.org/pdf/1707.01044 https://arxiv.org/pdf/1707.01044 An exact answer is desired since the final result reveals some structure that can be studied, and because it is very hard to get a numerical result due to the occurrence of spurious poles. For example, evaluating (1-x)/x - 1/x numerically is challenging around x=0 even though symbolically it can be made regular.

data_maan 2y ago
What do you mean by "symbolically it can be made regular"?
- eigenket 2y ago
  (1-x)/x - 1/x =1/x - 1 - 1/x = -1 Evaluating the expression naively near zero you're going to get wild numerical errors, but if you do the symbolic manipulation you're going to notice that it's just equal to -1. Edit: e.g. consider this interaction I just had with the python interpreter >>> x=1e-15 >>> (1-x)/x - 1/x -1.0 >>> x=1e-16 >>> (1-x)/x - 1/x 0.0 you get completely the wrong answer when x = 1e-16